Interactions between computability theory and set theory
- Author(s): Schweber, Noah
- Advisor(s): Montalban, Antonio
- et al.
In this thesis, we explore connections between computability theory and set theory. We investigate an extension of reverse mathematics to a higher-order context, focusing in particular on determinacy principles, and an extension of computable structure theory to uncountable structures via set-theoretic forcing. We also look at computability-theoretic operations induced by ultrafilters, and the classical computable structure theory of ordinals as clarified by set-theoretic results.